EVERY CFT$_3$ HAS AN $ \mathcal{L}_{\Lambda}w_{1+\infty}$ SYMMETRY

Andrew Strominger; Hongji Wei

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arXiv · 2603.26459

EVERY CFT$_3$ HAS AN $ \mathcal{L}_{\Lambda}w_{1+\infty}$ SYMMETRY

Andrew Strominger·Hongji Wei

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Abstract

Recently a one-parameter family of deformed $ \mathcal{L} w_{1+\infty}$ soft symmetry algebras, denoted $ \mathcal{L}_{\Lambda}w_{1+\infty}$, acting on tree-level gravitational theories in AdS$_4$ has been discovered. Here we show that all CFT$_3$s, including those dual to quantum gravity on AdS$_4$, admit an $\mathcal{L}_{\Lambda}w_{1+\infty}$ action generated by the ANEC operator, its conformal descendants and their commutators. This extends the previous tree-level results on these soft symmetries to the strongly-coupled quantum regime.

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Andrew Strominger, Hongji Wei. 2026-03-27. EVERY CFT$_3$ HAS AN $ \mathcal{L}_{\Lambda}w_{1+\infty}$ SYMMETRY. https://arxiv.org/abs/2603.26459

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